Official population forecasts, such as those produced by the U.S. Office of the Actuary, Social Security Administration, for the Bureau of the Census, provide the user with three forecast variants: high, middle, and low. However, the probability with which the future fails between the high and the low numbers is not reported and is not even known by the government forecasters. The proposed research will show how to produce high and low numbers that will encompass the future with know probabilities. Such probabilistic prediction intervals can be produced for national populations to replace or complement the current forecast variants produced by the government agencies. A novel feature in the proposed research is that we extend our past results to the so-called functional forecasts, i.e., to forecasts of some functions of the population vector. An example of such a (random) function is the number of disabled in a given time. Public and private decision-makers rely on various demographic forecasts to plan for the future and to anticipate the costs of new programs to care for the nation's aging population. Better societal and private decisions can by made if the decision-makers are aware of the extent of the uncertainty of the forecasts. The aims of the proposed research, namely to improve our understandings of the limitations of government forecasts, are intended to lead both to better forecasts and to better use the forecasts by decision makers. The research will produce a computer program that will carry out the stochastic propagation of error, which is necessary for assessing the uncertainty of the forecasts. The program will be usable by health agencies preparing forecasts based on the cohort-component method. The research will also produce a monograph that will describe the statistical theory of error propagation for these forecasts and will provide guidance for the use of the computer programs.